Aim: What’s so special about a 300-600-900 triangle? Do Now: Triangle ABC is equilateral with each side equal to 2x. CD is an altitude of ABC. What is mA? mB? mACB? What is mACD? mBCD? 600 C 300 2x 2x A B D 2x

Pythagorean Theorem - a2 + b2 = c2 300-600-900 triangle Triangle ABC is equilateral with each side equal to 2x. CD is an altitude of ABC What is length of CD in terms of x? C 300 2x 2x Pythagorean Theorem - a2 + b2 = c2 ? A 600 B x 2x D x2 + (CD)2 = (2x)2 x2 + (CD)2 = 4x2 (CD)2 = 3x2

Pythagorean Theorem - a2 + b2 = c2 300-600-900 triangle Triangle ABC is equilateral with each side equal to 6 (instead of 2x). CD is an altitude of ABC What is length of CD? C 300 Pythagorean Theorem - a2 + b2 = c2 6 6 ? A 600 B 32 + (CD)2 = (6)2 3 D 9 + (CD)2 = 36 (CD)2 = 27

Review the results of the first two problems. 300-600-900 triangle Problem 1 Problem 2 A 6 3 C D A C 2x x D 3 300 300 600 600 Review the results of the first two problems. Can you make any general conclusions?

300-600-900 triangle 300 2s 600 s

Pythagorean Theorem - a2 + b2 = c2 45o - 45o - 90o triangle Triangle ABC is an isosceles right triangle with BC = A. What is mB? mC? AB? AC? Do Now: C 450 x 2 A B Pythagorean Theorem - a2 + b2 = c2 x2 + x2 = ( )2 2x2 = ( )2 2x2 = 8

Pythagorean Theorem - a2 + b2 = c2 45o - 45o - 90o triangle Triangle ABC is an isosceles right triangle with BC = A. What AB? AC? Do Now: 2 6 6 C 2 6 x A B Pythagorean Theorem - a2 + b2 = c2 x2 + x2 = ( )2 2 6 2x2 = 72 x2 = 36 x = 6

Review the results of the first two problems. 300-600-900 triangle Problem 1 Problem 2 C C 2 6 A B A B Review the results of the first two problems. Can you make any general conclusions?

450- 450 - 900 triangle In a 450-450-900 triangle, the length of the hypotenuse is times the length of a leg. 450 s 450 s Ratio of Hypotenuse : Leg of I.R.T is always

Isosceles Right Triangle BF AB = 1.4142 . . = 2 450 CG AC = 1.4142 . . = 2 DH AD = 1.4142 . . = 2 EI AE = 1.4142 . . = 2 Ratio of Hypotenuse : Leg of I.R.T is always

Summary of Special Angles in Trig

Triangle ABC is a 30-60-90 triangle with BC = 7 A. What is length of Model Problem Triangle ABC is a 30-60-90 triangle with BC = 7 A. What is length of AB? AC? Do Now: C 300 7 3.5 A 600 B 3.5 Hypotenuse is 2 times the shorter leg CB = 2(AB) 7 = 2(AB) 3.5 = AB Longer leg is times the shorter leg AC = (AB) 3 AC = (3.5) 3 AC  6.06

Pythagorean Theorem - a2 + b2 = c2 Model Problem Triangle ABC is an isosceles right triangle with BC = 8 A. What AB? AC? Do Now: C 8 x A B Ratio of Hypotenuse : Leg of I.R.T is always Pythagorean Theorem - a2 + b2 = c2 x2 + x2 = (8)2 2x2 = 64 x2 = 32 x = 32 2 4 Instead of

Regents Prep What is the exact sum of + 0

Model Problem The rhombus below is a glass panel for a door. How many square inches of colored glass will you need for the panel? A = bh 6 in. 600 Draw an altitude of the rhombus. Label x and h as shown x h 6 in. 6 in. 600 Hypotenuse is 2 times the shorter leg 6 = 2x 3 = x Longer leg is times the shorter leg A = bh = 6( ) = 31.2 in2 h =

Model Problem A baseball diamond is a square. The distance from base to base is 90 ft. To the nearest foot, how far does the second baseman throw a ball to home plate? hypotenuse is times the length of a leg. 2 90’ Isosceles Right Triangle 90’  90 = 127.27922’ 2